Mortdecai: mort de cinéma, more like. It’s hard to think of a way in which the experience of watching the newJohnny Depp film could be any worse, unless you returned home afterwards to discover that Depp himself had popped round while you were out and set fire to your house. This is comfortably the actor’s worst film since Alice in Wonderland, and even dedicated fans will find their hearts shrivelling up like week-old party balloons at its all-pervading air of clenched desperation.

David Koepp’s film, which is based on the half-forgotten Charlie Mortdecai comic novels by Kyril Bonfiglioli, is a psychotically unfunny art-heist romp in which a broke aristocrat (Depp) prances round England and California on the trail of a missing painting, while Jock Strapp (Paul Bettany), his Kato-like manservant, remains either a few steps behind or ahead.

Depp’s performance doesn’t go much further than a passable Terry-Thomas impression, and the film’s make-up artists have even given him a lascivious gap between his top front teeth, just to hammer the likeness home. But the film’s conception of jet-setting glamour and intrigue is pure Alan Partridge: thoroughbred horses, corduroy blazers and bikini-clad models tottering randomly across the set.

“Lucky saddle,” Mortdecai simpers when he spots Olivia Munn’s wealthy heiress cantering across the lawn of some bleached Los Angeles villa – which, if you missed the zinger about underage sex a few minutes earlier, tells you all you need to know about the extent of the film’s comic ambitions. Other jokes are effectively normal lines of dialogue read in a silly accent. During a car chase that seems to take place entirely on motorway exit ramps, Mortdecai ends up on the vehicle’s bonnet and shouts: “I’m on the bonnet!”

But other actors who really should have known better must share in Depp’s disgrace. Gwyneth Paltrow is all bum and teeth as Johanna, Mortdecai’s boringly glamorous wife, whose dislike of her husband’s moustache prompts a bewilderingly in-depth subplot, while Ewan McGregor all but walks around with his head in his hands in the straight man role of a police inspector who calls on Mortdecai to help track down the stolen portrait. Jeff Goldblum is also in it for a scene or two until his character gets shot, and part of you wonders if Goldblum pulled the trigger himself when he read the next page of the script.

What’s fascinating about the film, other than its early and near-impregnable status as the worst of 2015, are its superficial but nagging similarities to Wes Anderson’sThe Grand Budapest Hotel, a project to which Depp was once attached. Both films centre on fey but sexually rapacious men who belong to bygone eras, and both involve a missing art treasure. Perhaps in a parallel universe, Ralph Fiennes missed a train by a fraction of a second, and Depp is now the star of a tragicomic Academy Award nominated masterpiece, while Fiennes gropes co-stars half his age and jokes about statutory rape.